Slow convergence in generalized central limit theorems
Slow convergence in generalized central limit theorems
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广义中心极限定理的缓慢收敛
DOI：
10.1016/j.crma.2018.04.013
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发表时间：
2017
影响因子：
0.8
通讯作者：
C. Greengard
中科院分区：
文献类型：
--
作者：
Christoph Borgers;C. Greengard
在气体及相关领域的动力学理论中，有许多涉及对数标度的极限定律。我们对这一主题的兴趣是由 Börgers 等人发起的。[2]，我们研究了由平行板界定的区域中自由分子流的演化，边界上有麦克斯韦反射。使用概率方法，我们表明，在消失间隙高度的限制下，扩散发生在“异常”时间尺度 1/(h| logh|) 上，其中 h 是板的适当无量纲分离。最近，Chumley 等人[5]对于非常广泛的几何形状中的相关动力学问题，已经获得了标准和异常的扩散结果。异常扩散结果
In the kinetic theory of gases and related areas, there are a number of limit laws that involve logarithmic scaling. Our interest in the subject was initiated by Börgers et al.[2], where we studied the evolution of free molecular flow in a region bounded by parallel plates with Maxwellian reflection on the boundaries. Using probabilistic methods, we showed that in the limit of vanishing gap height, diffusion occurs on the “anomalous” time scale 1/(h| logh|), where h is the properly non-dimensionalized separation of the plates. More recently, Chumley et al.[5] have obtained diffusion results, both standard and anomalous, for related kinetic problems in a very broad class of geometries. Anomalous diffusion results